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A Novel Approach to Characterizing LiDAR Waveforms Geoffrey M. Henebry Eric Ariel L. Salas Geographic Information Science Center of Excellence South Dakota State University and Naikoa Aguilar-Amuchastegui Department of Environmental Studies University of North Carolina-Wilmington [Forest Carbon Lead Scientist, World Wildlife Fund, as of 8/2010] Research supported through the NASA Biodiversity program: NNX09AK23G. Thank you!

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Synergistic Analyses of Data from Active and Passive Sensors to Assess Relationships between Spatial Heterogeneity of Tropical Forest Structure and Biodiversity Dynamics Study site: Tropical forests on the Atlantic slope of Costa Rica, specifically, the stands under sustainable management by FUNDECOR, a Costa Rican NGO. Project proposed: 6/2008 Project funding received: 7/2009 First field campaign:6/2010 Focus today on a new approach that we very recently developed for characterizing LiDAR waveform data.

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The Challenge of Analyzing LiDAR Waveforms - 1 LiDAR (Light Detection And Ranging) is an active remote sensing technology that 1.Uses laser light to illuminate the target area, 2.Senses backscattering of the illuminating radiation, and 3.Measures the time a laser pulse takes to travel back from regions of strong backscattering. A LiDAR waveform sensor records the power of the backscattering signal at fine temporal resolution which can be converted to distance. Thus, the term laser altimetry; LiDAR measures altitudes.

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The Challenge of Analyzing LiDAR Waveforms - 2 But we are more interested in knowing elevations: Terrain elevation above or below the waterline Vegetation height the crown of a specific tree or the nominal height of a canopy Vertical profile through a multilayered canopy resolving foliage densities to characterize habitat structure The mapping from altitudes to elevations is complicated by many confounding factors.

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The Challenge of Analyzing LiDAR Waveforms - 3 Waveform data have been actively collected for more than 15 years. Analyses of detected waveforms have been approached in three ways: 1.Multiple Gaussian curves fit to approximate the waveform; 2.Metrics relating the backscattering power to the cumulative distribution of backscattered illumination, such as HOME (height of median energy); and 3.Descriptive statistics on the waveform. I contend there is a richness in LiDAR waveforms that has yet to be exploited by conventional analyses.

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Assume that the waveform is displayed in Cartesian coordinates with the abscissa displaying time lapse t and ordinate displaying backscattered power p. t p

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P Selected Pivots Left PivotRight Pivot MD LP to 1 st Max. Power MD LP to Dip MD LP to 2 nd Max. Power MD can be computed from RP. MD LP to RP MD can be computed from LP to any point on the curve. More points give better shape definition. MD RP to 2 nd Max. Power MD RP to Dip MD RP to 1 st Max. Power MD RP to LP Moment Distance Method - 1 Let the subscript LP denote the left pivot or earlier temporal reference point and subscript RP denote the right pivot or later temporal reference point. t

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Moment Distance Method - 2 The MD framework is described in the following pair of equations: The moment distance from the left pivot (MD LP ) is the sum of the hypotenuses constructed from the left pivot to the power at successively later times (index i from t LP to t RP ): one base of each triangle is the difference from the left pivot (i – t LP ) along the abscissa and the other base is simply the power at i. Similarly, the moment distance from the right pivot (MD RP ) is the sum of the hypotenuses constructed from the right pivot to the power at successively earlier times (index i from t RP to t LP ): one base of each triangle is the difference from the right pivot (t RP – i) along the abscissa and the other base is simply the power at i. [1] [2]

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In the 1998 La Selva waveform, there are 133 points on the curve between the LP and RP and the MDI = In the 2005 La Selva waveform, there are 153 points on the curve between the LP and RP and the MDI = Moment Distance Method - 3 From this pair of moment distances, we form the Moment Distance Index (MDI) and the MDI Normalized (MDIN): MDI = MD LP – MD RP [3] MDIN = MDI / (MD LP + MD RP ) [4] We propose that MDI can be used to capture dynamics in canopy structure.

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Three waveform types found in LVIS data from La Selva  Max Peak Early  Max Peak Late  Equal Peaks MDI vs. waveform landmarks Location of early max peak Power of early max peak Power of late max peak

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Time series of waveform landmarks and MDIs calculated using a time series of simulated LiDAR returns from a 30m x 30m forest stand grown in silico with Zelig, a spatially-explicit forest gap model developed by Dr. Dean Urban, Duke. Data courtesy of Dr. Guoqing Sun, NASA/GSFC. Note that shortly after year 120, the “first peak” disappears and does not reappear until about year 240. There is an interpretation of these results that links MDI to the succession of peaks.

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Concluding Thoughts The Moment Distance framework and the Moment Distance metrics offer a new and simple approach to characterizing LiDAR waveforms. We are exploring several questions: How to select the pivots? How to select the range(s) of interest? How to process the waveform before MD analysis? When is MDIN or other MD metrics preferred to MDI? What are the effects of noise? What are the effects of sloping terrain? What are the temporal phenomenologies of MD metrics? Early days, but I will venture this approach will become very useful for mapping waveforms to habitat structure and linking with organismal occurrence/abundance data.